This application claims the priority of German Patent Application, Serial No. 102 09 141.2, filed Mar. 1, 2002, pursuant to 35 U.S.C. 119(a)-(d), the disclosure of which is incorporated herein by reference.
The invention relates to a method for calibrating and operating machine units in machine tools and robotic devices that perform a parallel-kinematic motion in a motion space.
The term xe2x80x9cparallel-kinematicxe2x80x9d is used to describe machines with drives, wherein the position of a machine unit relative to a reference system can be derived from the totality of the positions of all drives operating in parallel on the machine unit, wherein each drive exclusively moves a single drive train relative to the reference system which is associated with this drive.
Machine units that are moved by a parallel kinematics can have a different number of degrees of freedom, depending on the design and number of drives and additional constraints, such as bearings and guides. As with classical (i.e., serial machine kinematics) a kinematic degree of freedom of a moved machine unit is defined by each drive which is typically uniaxial. However, unlike the serial machine kinematics, individual drives cannot be associated with individual degrees of freedom of the machine unit.
Parallel-kinematics are employed with machine tools, but can also have other applications, for example in robotic devices, which are described, for example, in U.S. Pat. No. 6,328,510 B1, which is incorporated herein by reference in its entirety.
The simplest calibration method according to the state-of-the-art includes a very precise measurement of all individual components as well as the entire assembly. This method has a disadvantage that it is very complex and not very precise, since the individual errors typically add up to a larger total error.
Other conventional methods determine corrected parameter values based on measured positioning errors in the Cartesian coordinate system by starting from a raw transformation based on measured parameters or based on fabrication dimensions. Such methods are described, for example, in WO 99/28097 and DE 19 80 6085 A1. Because the kinematic transformation typically involves rather complex transcendent functions, the corrected parameter values are computed mostly with numeric equation solvers and/or with numeric optimization methods. These methods include the so-called descent methods, with the Newton-method being the most widely known method.
It is evident that a parallel-kinematic machine can only be as accurate as the information about the underlying transformation and the transformation parameters, unless an error compensation method, for example in the Cartesian coordinate system, is employed. All calibration methods, with the exception of the error compensation methods, aim to exactly determine the transformation parameters. Conversely, in the error compensation method, a table with the compensation values associated with the different corresponding positions is stored and taken into account when computing the desired positions values. For positions between the support points in the table, the compensation values are interpolated.
Disadvantageously, these error compensation methods can only be calibrated in the region of the workspace where measurement values are available. Because of the non-linear nature of the transformation, these measurement support points have to be located on the fine grid (e.g., every 10 mm), which causes long measuring times. However, if all transformation parameters are determined with sufficient accuracy, then the operating precision of the machine improves also outside of the regions where measurement values are available. This method for determining the transformation parameters is therefore typically preferred over error compensation methods.
It would therefore be desirable and advantageous to provide an improved method for calibrating and operating machine units in machine tools and robotic devices that perform a parallel-kinematic motion in a motion space, which obviates prior art shortcomings and is able to specifically provide less computation-intensive convergent solutions.
The invention is directed to a method for calibrating parallel-kinematic machine units, and more particular to a method that uses an iterative process for generating a kinematic transformation. The method is robust and uses an iterative solution trial based on a simple and robust algorithm, wherein the measurement of the machine is integrated in the integration cycle and therefore executed multiple times. Advantageously, the number of integration cycles is small so that the method can be automated.
According to an aspect of the invention, a method is disclosed for calibrating machine units disposed in machine tools and robotic devices and moved by a parallel kinematic in a motion space. The machine units including between two and six drives that can be controlled independently of each other, either directly or via force transmitting and guide means or articulated joints that operate on a moved machine unit. A controller can set desired positions and/or desired trajectories in a Cartesian coordinate system and/or convert the Cartesian desired positions and desired trajectories into desired positions and/or desired trajectories of the two to six drives through a kinematic transformation {right arrow over (g)}, depending of a finite set of invariant machine parameters. The machine units can also include measurement and control devices for controlling the two to six drives to their desired positions and/or desired trajectories, and a device for measuring a deviation of an actual position from the position set by the controller.
The method according to the present invention includes the steps of:
a) determining on a number of K positions in the motion space of the moved machine unit the deviation of the actual position from the position set by the controller,
b) linearizing for each position k of the K positions the nonlinear relationship between parameters errors and positioning errors by way of a Jacobi matrix Jk,
c) forming a system of linear equations between parameters errors and positioning errors from the K linearized relationships,
d) computing the parameter error by at least approximately solving the system of linear equations,
e) computing new machine parameters from the machine parameters used in the transformation {right arrow over (g)} with the computed parameter errors, and
f) updating the kinematic transformation {right arrow over (g)} stored in the controller with the updated machine parameters.
Advantageous embodiments of the method may include one or more of the following features. The number K of measurements can be selected so that the system of linear equations has a unique solution. However, the number K of measurements can also be greater than necessary to produce a system of linear equations with a unique solution, in which case the system of linear equations can be solved approximately using a least-squares method.
Advantageously, the parameter errors can be computed by including historic statistical data of measurement values and estimated parameter errors with a minimal variance. Also, new machine parameters can be computed by associating a weight with the parameter errors. A linearization can be performed about the machine parameters that form the basis of the kinematic transformation {right arrow over (g)} and are stored in the controller.
To reduce the mathematical complexity, the Jacobi matrix Jk can be calculated numerically by using a difference quotient, either by using the kinematic transformation {right arrow over (g)} stored in the controller as well as the Cartesian desired positions of the machine unit, or by using the indirect kinematic transformation {right arrow over (f)} with the actual positions of the drive.
The method steps a) through f), as set forth above, can be repeated until the positioning error is smaller than a predetermined value, wherein during the subsequent repetition of steps a) through f) the positioning error can either be newly measured or computed with a predictive method based on a modified transformation. Alternatively or in addition, the steps a) through f) above may be repeated only until a positioning accuracy is achieved which requires a lesser number of support points than an error compensation without a prior application of the disclosed method. The error compensation is then performed with the reduced number of support points by repeating steps a) through f) and either newly measuring the positioning error or computing the positioning error with a predictive method based on a modified transformation.
The errors can be compensated in a Cartesian coordinate system or in a coordinate system of the axes drives.
For measuring the positioning error, a master workpiece with machining features can be scanned. The master workpiece can be, for example, a plate, and the machining features can be implemented as bores having a known position, a known diameter and a known depth. The positioning error can be measured with a measuring device, such as a stylus, laser interferometer and/or laser tracker.
Because the algorithm is simple, it can also be executed autonomously on the computer of the machine controller, which is advantageous in manufacturing applications by obviating the need for external computers.